# Suboscillations with arbitrary shape

## TL;DR

This paper introduces a method to construct bandpass functions that can approximate any analytic function with high accuracy, demonstrating the counter-intuitive phenomenon of suboscillations where functions oscillate slower than their minimum frequency component.

## Contribution

The paper presents a novel technique for creating bandpass functions capable of suboscillations, expanding the understanding of oscillatory behavior in signal processing.

## Key findings

- Bandpass functions can approximate any analytic function with arbitrary accuracy.
- Suboscillations can occur where functions oscillate slower than their lowest frequency component.
- The method demonstrates the feasibility of designing such functions with practical applications.

## Abstract

We report a method for constructing bandpass functions that approximate a given analytic function with arbitrary accuracy over a finite interval. A corollary is that bandpass functions can be obtained that oscillate arbitrarily slower than their minimum frequency component, a counter-intuitive phenomenon known as suboscillations.